Space Partitioning for Broad Sweep Collision Detection Part 2 - Quadtrees

1. Space Partitioning for Broad Sweep Collision DetectionPart 2 - Quadtrees Game Design Experience Professor Jim Whitehead February 13, 2009 Creative Commons Attribution 3.0creativecommons.org/licenses/by/3.0

2. Announcements • Technical Design Document • Due today • May turn it in to the box by my door by the end of the day • Have midterm exams • See me after class to pick up • Answer key is on class website

3. Broad vs Narrow Sweep • With many small objects in large playfield • Each object only has the potential to collide with nearby objects • Broad sweep • Perform a quick pass over n objects to determine which pairs have potentialto intersect, p • Narrow sweep • Perform p x p check of objectpairs that have potential tointersect • Dramatically reduces # of checks Mushihimesama

4. Broad sweep approaches • Grid • Divide playfield into a grid of squares • Place each object in its square • Only need to check contents of square against itself and neighboring squares • See http://www.harveycartel.org/metanet/tutorials/tutorialB.html for example • Space partitioning tree • Subdivide space as needed into rectangles • Use tree data structure to point to objects in space • Only need to check tree leaves • Quadtree, Binary Space Partition (BSP)tree • Application-specific • 2D-shooter: only need to checkfor collision against ship • Do quick y check for broad sweep Point Quadtree (Wikipedia)

5. Trees root • A tree is a data structure • Places contents into nodes • Each node has • Contents • Pointers to 0 or more other levels • Children are represented as references 56 a b 45 75 d c 24 51 // A simple tree node class Class Node { List<Node> children; // List of references to Nodes int contents; } A tree with 5 nodes (root, a, b, c, d).Root node has contents 56.Node a has contents 45, and two children, c and d.Node b has contents 75, and no children.Node c has contents 24, and no children.Node d has contents 51, and no children.

6. Tree Operations • Adding a child • Create new node • n = new Node(); • Add it to list of children of parent • parentNode.children.Add(n); • Removing a child • Find and remove child node from list of children • parentNode.children.Remove(childToRemove); • (childToRemove is reference to Node of child to be deleted)

7. Point Quadtree root • A tree where each node has four children • Each level represents subdividing space into 4 quadrants • Each node holds information about one quadrant • A deeper tree indicates more subdivisions MX Quadtree Demo http://donar.umiacs.umd.edu/quadtree/points/mxquad.html Demo both points and rectangles 0 1 0 3 1 2 2 3 root 1.1 1.0 0 3 1 2 0 1 1.2 1.3 1.0 1.1 1.2 1.3 2 3

8. C# Node Representation class Node { Point min[4]; Point max[4]; int level; Node Quad[4]; // holds 4 quadrants List<IGameObject> objectList; // list of game objects in a Node } • quads is an array with four elements • Each element is a reference to a Node • Quad[0] – upper left, etc. • A recursive data structure • Nodes hold pointers to Nodes • Min[] is an array with four elements • Each element is upper left point of quadrant • Max[] holds lower right point of each quadrant • Level indicates how many levels down in the tree • Useful for bounding the depth of the tree Quad[0] Quad[1] Quad[2] Quad[3]

9. Adding object to tree Insert(Node n, IGameObject g) • Iterate through all 4 quadrants of current node (n) • If at maximum depth of the tree • Add IGameObject to objectList and return • If AABB (bounding box) of IGameObject lies fully within a quadrant • Create child node for that quadrant, if necessary • Then call insert on that node (recursion) • Otherwise, AABB does not lie in just one quadrant • Add to contents list at this level • First call is Insert(root, g) • That is, start at root node for insertions

10. Finding, removing object in tree Find(Node n, IGameObject g) • Iterate through all 4 quadrants of current node (n) • Check if AABB (bounding box) of IGameObject spans multiple quadrants • Yes: IGameObject is in this node. Return node. • At maximum level of tree? • Yes: IGameObject is at this level • If AABB (bounding box) of IGameObject lies fully within a quadrant • Call find on that node (recursion) • Removing object from tree • Found_node = Find(root, g) • Found_node.objectList.Remove(g)